- Docente: Daniele Ritelli
- Credits: 8
- SSD: SECS-S/06
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Financial Markets and Institutions (cod. 0901)
Learning outcomes
Mathematical tools in measure theory and differential equations in view of applications in Mathematical finance
Course contents
Lebesgue measure and Lebesgue integral. Abstract measure.
Probability measure.
Beppo Levi's Theorem (monotone convergence), Fatou's Lemma,
dominated convergence Theorem. Derivation of integrals dependent by
a parameter.
Integration in product spaces: Fubini's Theorem. Decomposition
of integrals on R^2. Change of variable. Absolute continuity:
Radon-Nikodym Theorem. Lebesgue Stieltjes measure.
Review of some useful special functions: Euler Gamma and
Beta.
Ordinary differential equations of first order: linear and
separable. Second order linear differential equations.
Partial differential equations: the heat equation integrated
by means of Fourier transform and Gamma function.
Readings/Bibliography
M. Capinski and E. Kopp: Measure, Integral and Probability.
Springer 2004
D. Sondermann: Introduction to Stochastic Calculus for Finance.
Springer 2006
B. Osgood: The Fourier Transform and its Applications. Lecture
notes available at
http://arni.epfl.ch/_media/courses/circuitsandsystems2011/book-2009.pdf
R.P. Aagarwal, D, O'Reagan: Ordinary and Partial Differential
Equation: Springer 2008, lessons 1, 41, 42, 43
H. Hsu: Probability, Random Variables and Random Processes,
MacGraw Hill
Teaching methods
Lessons ex Cathedra. Homework
Assessment methods
Written examination
Teaching tools
Video beamer
Links to further information
http://www.danieleritelli.name
Office hours
See the website of Daniele Ritelli